4.1.1 Visual exploration - Univariate Analysis

recipes %>% 
  ggplot(aes(x=as.factor(rating), fill=as.factor(rating) )) +  
  geom_bar( ) +
  scale_fill_manual(values = c("red4", "red3", "orangered", "orange", "gold", "greenyellow", "green3", "green4") ) +
  theme(legend.position="none") +
  scale_y_continuous(breaks=seq(0,10000,1000)) +
  labs(x = "Rating", y = "Number of recipes", 
       title = "Overview of recipes' ratings")

recipes_plot <- recipes %>% 
  pivot_longer(cols = c(calories, protein, fat, sodium),
               names_to = "nutrition",
               values_to = "n_value")

# Calories boxplot not filtered
recipes_plot %>%
  filter(nutrition == "calories") %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme_light() +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  ggtitle("Boxplot of calories nutritional value") +
  xlab("") +
  ylab("Value")

recipes_plot %>% 
  filter(nutrition == "calories") %>% 
  select(title, nutrition, n_value) %>% 
  arrange(desc(n_value)) 

#> # A tibble: 10,321 x 3
#>    title                                            nutrition n_value
#>    <chr>                                            <chr>       <dbl>
#>  1 "Pear-Cranberry Mincemeat Lattice Pie "          calories   3.01e7
#>  2 "Deep-Dish Wild Blueberry Pie "                  calories   3.00e7
#>  3 "Apricot, Cranberry and Walnut Pie "             calories   1.31e7
#>  4 "Lamb Köfte with Tarator Sauce "                 calories   4.52e6
#>  5 "Rice Pilaf with Lamb, Carrots, and Raisins "    calories   4.16e6
#>  6 "Chocolate-Almond Pie "                          calories   3.36e6
#>  7 "Caramelized Apple and Pear Pie "                calories   3.36e6
#>  8 "Merguez Lamb Patties with Golden Raisin Cousco~ calories   5.45e4
#>  9 "Grilled Lamb Chops with Porcini Mustard "       calories   2.41e4
#> 10 "Braised Short Ribs with Red Wine Gravy "        calories   1.96e4
#> # i 10,311 more rows

# Calories boxplot
df <- recipes_plot %>%
  filter(nutrition == "calories", n_value <= 7000)

boxplot_calories <- df %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
  geom_boxplot()+
  scale_fill_viridis(discrete = TRUE, alpha=0.6) +
  theme(legend.position="none",
        plot.title = element_text(size=11)) +
  scale_y_continuous(breaks=seq(0,7000,500)) +
  labs(x = "", y = "Calories", title = "Boxplot of calories nutritional value filtered")


# Calories histogram
histogram_calories <- df %>% 
  ggplot(aes(x=n_value)) +
  geom_histogram(binwidth=50, fill="red3", color="red3", alpha=0.9) +
  theme(plot.title = element_text(size=11)) +
  scale_x_continuous(breaks=seq(0,10000,1000)) +
  scale_y_continuous(breaks=seq(0,1750,250)) +
  labs(x = "Count", y = "Calories", title = "Distribution of calories across all recipes")


# Calories density plot
density_calories <- df %>% 
  ggplot(aes(x=n_value)) +
  geom_density(fill="red3", color="red2", alpha=0.8) +
  theme(plot.title = element_text(size=11)) +
  scale_x_continuous(breaks=seq(0,10000,1000)) +
  ggtitle("Distribution of calories across all recipes") +
  xlab("Calories")

grid.arrange(boxplot_calories, histogram_calories, density_calories, ncol=2, nrow =2)

recipes_plot %>%
  filter(nutrition == "protein") %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme_light() +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  ggtitle("Boxplot of protein nutritional value") +
  xlab("") +
  ylab("Value")

recipes_plot %>%
  filter(nutrition == "protein") %>% 
  select(title, nutrition, n_value) %>% 
  arrange(desc(n_value)) 

#> # A tibble: 10,321 x 3
#>    title                                            nutrition n_value
#>    <chr>                                            <chr>       <dbl>
#>  1 "Rice Pilaf with Lamb, Carrots, and Raisins "    protein    236489
#>  2 "Pear-Cranberry Mincemeat Lattice Pie "          protein    200968
#>  3 "Deep-Dish Wild Blueberry Pie "                  protein    200210
#>  4 "Lamb Köfte with Tarator Sauce "                 protein    166471
#>  5 "Apricot, Cranberry and Walnut Pie "             protein     87188
#>  6 "Chocolate-Almond Pie "                          protein     58334
#>  7 "Caramelized Apple and Pear Pie "                protein     58324
#>  8 "Merguez Lamb Patties with Golden Raisin Cousco~ protein      2074
#>  9 "Manhattan Clam Chowder "                        protein      1625
#> 10 "Clam and Oyster Chowder "                       protein      1365
#> # i 10,311 more rows

# Proteins boxplot
boxplot_protein <- recipes_plot %>%
  filter(nutrition == "protein", n_value <= 1000) %>% 
  ggplot( aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  scale_y_continuous(breaks=seq(0,7000,25)) +
  ggtitle("Boxplot of protein nutritional value filtered") +
  xlab("") +
  ylab("Proteins") 


# Proteins histogram
histogram_protein <- recipes_plot %>% 
  filter(nutrition == "protein", n_value <= 1000) %>% 
  ggplot(aes(x=n_value)) +
  geom_histogram(binwidth=7, fill="red3", color="red3", alpha=0.9) +
  theme(plot.title = element_text(size=15)) +
  scale_x_continuous(breaks=seq(0,1000,50)) +
  scale_y_continuous(breaks=seq(0,7000,250)) +
  ggtitle("Distribution of proteins across all recipes") +
  xlab("Proteins") +
  ylab("Count") 


# Protein density plot
density_protein <- recipes_plot %>% 
  filter(nutrition == "protein", n_value <= 1000) %>% 
  ggplot(aes(x=n_value)) +
  geom_density(fill="red3", color="red2", alpha=0.8) +
  scale_x_continuous(breaks=seq(0,1000,50)) +
  ggtitle("Distribution of proteins across all recipes") +
  xlab("Proteins")

grid.arrange(boxplot_protein, histogram_protein, density_protein, ncol=2, nrow =3)

recipes_plot %>%
  filter(nutrition == "sodium") %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  ggtitle("Boxplot of sodium nutritional value") +
  xlab("") +
  ylab("Value")

recipes_plot %>% 
  filter(nutrition == "sodium") %>%
  select(title, nutrition, n_value) %>% 
  arrange(desc(n_value)) 

#> # A tibble: 10,321 x 3
#>    title                                           nutrition  n_value
#>    <chr>                                           <chr>        <dbl>
#>  1 "Pear-Cranberry Mincemeat Lattice Pie "         sodium    27675110
#>  2 "Deep-Dish Wild Blueberry Pie "                 sodium    27570999
#>  3 "Apricot, Cranberry and Walnut Pie "            sodium    12005810
#>  4 "Lamb Köfte with Tarator Sauce "                sodium     7540990
#>  5 "Chocolate-Almond Pie "                         sodium     3449512
#>  6 "Caramelized Apple and Pear Pie "               sodium     3449373
#>  7 "Rice Pilaf with Lamb, Carrots, and Raisins "   sodium     3134853
#>  8 "Whole Branzino Roasted in Salt "               sodium      132220
#>  9 "Red Snapper Baked in Salt with Romesco Sauce " sodium      132025
#> 10 "Scallops with Mushrooms in White-Wine Sauce "  sodium       90572
#> # i 10,311 more rows

# Sodium boxplot
boxplot_sodium <- recipes_plot %>%
  filter(nutrition == "sodium", n_value <= 30000) %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  scale_y_continuous(breaks=seq(0,30000,500)) +
  ggtitle("Boxplot of sodium nutritional value") +
  xlab("") +
  ylab("Sodium") 


# Sodium histogram
histogram_sodium <- recipes_plot %>%
  filter(nutrition == "sodium", n_value <= 30000) %>% 
  ggplot(aes(x=n_value)) +
  geom_histogram(binwidth=50, fill="red3", color="red3", alpha=0.9) +
  theme(plot.title = element_text(size=15)) +
  scale_x_continuous(breaks=seq(0,30000,1000)) +
  scale_y_continuous(breaks=seq(0,1750,250)) +
  ggtitle("Distribution of sodium across all recipes") +
  xlab("Sodium") +
  ylab("Count") 


# Sodium density plot
density_sodium <- recipes_plot %>%
  filter(nutrition == "sodium", n_value <= 30000) %>% 
  ggplot(aes(x=n_value)) +
  geom_density(fill="red3", color="red2", alpha=0.8) +
  scale_x_continuous(breaks=seq(0,30000,1000)) +
  ggtitle("Distribution of sodium across all recipes") +
  xlab("Sodium") 


grid.arrange(boxplot_sodium, histogram_sodium, density_sodium, ncol=1, nrow =3)

recipes_plot %>%
  filter(nutrition == "fat") %>% 
  ggplot(aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme_light() +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  ggtitle("Boxplot of fat nutritional value") +
  xlab("") +
  ylab("Value")

recipes_plot %>% 
  filter(nutrition == "fat") %>% 
  select(title, nutrition, n_value) %>% 
  arrange(desc(n_value)) 

#> # A tibble: 10,321 x 3
#>    title                                           nutrition n_value
#>    <chr>                                           <chr>       <dbl>
#>  1 "Pear-Cranberry Mincemeat Lattice Pie "         fat       1722763
#>  2 "Deep-Dish Wild Blueberry Pie "                 fat       1716279
#>  3 "Apricot, Cranberry and Walnut Pie "            fat        747374
#>  4 "Rice Pilaf with Lamb, Carrots, and Raisins "   fat        221495
#>  5 "Chocolate-Almond Pie "                         fat        186660
#>  6 "Caramelized Apple and Pear Pie "               fat        186642
#>  7 "Lamb Köfte with Tarator Sauce "                fat         44198
#>  8 "Grilled Lamb Chops with Porcini Mustard "      fat          2228
#>  9 "Braised Short Ribs with Red Wine Gravy "       fat          1818
#> 10 "Braised Duck Legs with Shallots and Parsnips " fat          1610
#> # i 10,311 more rows

# Fat boxplot
boxplot_fat <- recipes_plot %>%
  filter(nutrition == "fat", n_value <= 40000) %>% 
  ggplot( aes(x=nutrition, y=n_value, fill=nutrition)) +
    geom_boxplot() +
    scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
    theme_light() +
    theme(legend.position="none",
          plot.title = element_text(size=11)) +
  scale_y_continuous(breaks=seq(0,3000,100)) +
  ggtitle("Boxplot of fat nutritional value filtered") +
  xlab("") +
  ylab("Fat") 


# Fat histogram
histogram_fat <- recipes_plot %>% 
  filter(nutrition == "fat", n_value <= 40000) %>% 
  ggplot(aes(x=n_value)) +
  geom_histogram(binwidth=7, fill="red3", color="red3", alpha=0.9) +
  theme(plot.title = element_text(size=15)) +
  ggtitle("Distribution of fat across all recipes") +
  scale_x_continuous(breaks=seq(0,3000,100)) +
  scale_y_continuous(breaks=seq(0,7000,250)) +
  xlab("Fat") +
  ylab("Count") 

# Sodium density plot
density_fat<- recipes_plot %>%
  filter(nutrition == "fat", n_value <= 40000) %>% 
  ggplot(aes(x=n_value)) +
  geom_density(fill="red3", color="red2", alpha=0.8) +
  scale_x_continuous(breaks=seq(0,3000,100)) +
  ggtitle("Distribution of sodium across all recipes") +
  xlab("Fat") 

grid.arrange(boxplot_fat, histogram_fat, density_fat, ncol=3)

4.1.2 Visual exploration - Multivariate Analysis

#removing 41 outliers we discovered above from the recipes df
recipes <- recipes %>% 
  filter(calories <= 7000, protein <= 1000, sodium <= 30000, fat <= 40000)


# Scatterplot of Rating-Calories
sp1 <- recipes %>% 
  ggplot(aes(x=calories, y=rating)) +
  geom_point(alpha=.5) +
  ggtitle("Scatterplot of rating against calories") +
  xlab("Calories") +
  ylab("Rating")

# Scatterplot of Rating-Protein
sp2 <- recipes %>% 
  ggplot(aes(x=protein, y=rating)) +
  geom_point(alpha=.5) +
  ggtitle("Scatterplot of rating against proteins") +
  xlab("Proteins") +
  ylab("Rating") 

# Scatterplot of Rating-Fat
sp3 <- recipes %>% 
  ggplot(aes(x=fat, y=rating)) +
  geom_point(alpha=.5) +
  ggtitle("Scatterplot of rating against fat") +
  xlab("Fat") +
  ylab("Rating") 

# Scatterplot of Rating-Sodium
sp4 <- recipes %>% 
  ggplot(aes(x=sodium, y=rating)) +
  geom_point(alpha=.5) +
  ggtitle("Scatterplot of rating against sodium") +
  xlab("Sodium") +
  ylab("Rating") 

grid.arrange(sp1, sp2, sp3, sp4, ncol=2, nrow =2)

corr_nutritional_values = recipes %>% 
  select(rating, calories, protein, fat, sodium) %>% 
  cor()

corrplot(corr_nutritional_values)

# Grouped scatter of calories and fat
recipes_plot1 <- recipes %>% 
  filter(fat <= 400, calories <= 6000) %>% 
  ggplot(aes(x=calories, y=fat, color=rating)) +
  geom_point(alpha=.5) + 
  scale_color_gradientn(colours = rainbow(5))

# Grouped scatter of calories and protein
recipes_plot2 <- recipes %>% 
  filter(protein <= 500, calories <= 6000) %>% 
  ggplot(aes(x=calories, y=protein, color=rating)) +
  geom_point(alpha=.5) + 
  scale_color_gradientn(colours = rainbow(5))

# Grouped scatter of protein and fat
recipes_plot3 <- recipes %>% 
  filter(fat <= 400, protein <= 350) %>% 
  ggplot(aes(x=protein, y=fat, color=rating)) +
  geom_point(alpha=.5) + 
  scale_color_gradientn(colours = rainbow(5))


# Grouped scatter of protein and sodium
recipes_plot4 <- recipes %>% 
  filter(sodium <= 400, protein <= 350) %>%  
  ggplot(aes(x=protein, y=sodium, color=rating)) +
  geom_point(alpha=.5) + 
  scale_color_gradientn(colours = rainbow(5))

grid.arrange(recipes_plot1, recipes_plot2, recipes_plot3, recipes_plot4, ncol=2, nrow =2)

4.2.1 Feature engineering

We discovered that the variable “drinks” on it’s own had only 11 observations, 4 of which also had the value “drink” equal to 1. Therefore, we decided to merge the two columns to simplify working with a single category called “drink” for all drinks.

#Creating a new dataframe with only the ID, title and the ingredients
ingredients_df <- recipes %>% 
  mutate(drink = ifelse(drink == 1 | drinks == 1, 1, 0)) %>% #merging drinks and drink
  select(ID, title, all_of(all_ingredients), rating)

ingredients_df_bin <- ingredients_df %>%
  mutate(vegetables_bin = as.numeric(if_any(all_of(vegetables_vec), ~.x == 1, na.rm = TRUE)),
         meats_bin = as.numeric(if_any(all_of(all_meats), ~.x == 1, na.rm = TRUE)),
         fish_bin = as.numeric(if_any(all_of(fish_vec), ~.x == 1, na.rm = TRUE)),
         seafood_bin = as.numeric(if_any(all_of(seafood_vec), ~.x == 1, na.rm = TRUE)),
         herbs_bin = as.numeric(if_any(all_of(herbs_vec), ~.x == 1, na.rm = TRUE)),
         nuts_bin = as.numeric(if_any(all_of(nuts_vec), ~.x == 1, na.rm = TRUE)),
         fruits_bin = as.numeric(if_any(all_of(fruits_vec), ~.x == 1, na.rm = TRUE)),
         cheese_bin = as.numeric(if_any(all_of(cheeses_vec), ~.x == 1, na.rm = TRUE)),
         dairy_bin = as.numeric(if_any(all_of(dairy_vec), ~.x == 1, na.rm = TRUE)),
         spices_bin = as.numeric(if_any(all_of(spices_vec), ~.x == 1, na.rm = TRUE)),
         cereals_bin = as.numeric(if_any(all_of(cereals_vec), ~.x == 1, na.rm = TRUE)),
         carbs_bin = as.numeric(if_any(all_of(carbs_vec), ~.x == 1, na.rm = TRUE)),
         dessert_bin = as.numeric(if_any(all_of(dessert_vec), ~.x == 1, na.rm = TRUE)),
         egg_bin = (egg)
         ) %>% 
  select(ID, title, contains("bin"), everything())

####testing if I still need to include the general category to create the binary column now that I modified the df to only include recipes with ingredients specified
# 
# #6586
# ingredients_df %>%
#   mutate(vegetables_bin = as.factor(as.numeric(if_any(c(vegetable, all_of(vegetables_vec)), ~.x == 1, na.rm = TRUE)))) %>%
#   filter(vegetables_bin == 1)
# 
# #6586
# ingredients_df %>%
#   mutate(vegetables_bin = as.factor(as.numeric(if_any(all_of(vegetables_vec), ~.x == 1, na.rm = TRUE)))) %>%
#   filter(vegetables_bin == 1)

ingredients_df_total <- ingredients_df %>%
  mutate(total_ingredients = rowSums(select(., c(all_of(all_ingredients)))),
         total_vegetables = rowSums(select(., c(all_of(vegetables_vec)))),
         total_meat = rowSums(select(., c(all_of(all_meats)))),
         total_fish = rowSums(select(., c(all_of(fish_vec)))),
         total_seafood = rowSums(select(., c(all_of(seafood_vec)))),
         total_herbs = rowSums(select(., c(all_of(herbs_vec)))),
         total_nuts = rowSums(select(., c(all_of(nuts_vec)))),
         total_fruits = rowSums(select(., c(all_of(fruits_vec)))),
         total_cheese = rowSums(select(., c(all_of(cheeses_vec)))),
         total_dairy= rowSums(select(., c(all_of(dairy_vec)))),
         total_spices= rowSums(select(., c(all_of(spices_vec)))),
         total_cereals= rowSums(select(., c(all_of(cereals_vec)))),
         total_carbs = rowSums(select(., c(all_of(carbs_vec)))),
         total_dessert = rowSums(select(., c(all_of(dessert_vec))))
         ) %>% 
  select(ID, title, contains("total"), everything())

total_join <- ingredients_df_total %>% 
  select(ID, contains("total"))
  
ingredients_df_full <- ingredients_df_bin %>% 
  left_join(total_join) %>% 
  select(ID, title, rating, contains("bin"), contains("total"), everything())

4.2.2 “Binary” engineered ingredients categories

#creating a vector with colnames of all the binary columns to be able to select them more easily afterwards
binary_columns <- ingredients_df_bin %>% 
  select(contains("bin")) %>% 
  colnames()

#adding binary columns to ingredients_df
total_categories <- ingredients_df_bin %>% 
  select(ID, all_of(binary_columns)) %>% 
  pivot_longer(-ID, names_to = "category", values_to = "binary_value") %>% 
  group_by(category) %>% 
  summarise(total = sum(binary_value))

#plotting the frequency of binary columns
total_categories %>%
  ggplot(aes(x=reorder(category,total), y=total, fill=total)) +
  geom_bar(stat = "identity") +
  scale_x_discrete(guide = guide_axis(n.dodge=3))+
  scale_fill_viridis() +
  labs(x = "Category", y = "Amount of recipes", title = "Total amount of recipes containing at least one ingredient in defined categories")

ingredients_df_bin %>% 
  select(contains("bin")) %>%
  mutate(across(everything(), as.factor)) %>% 
  plot_bar(order_bar = FALSE)

ingredients_df_bin %>% 
  select(contains("bin"), rating) %>%
  mutate(across(everything(), as.factor)) %>% 
  plot_bar(by = "rating", order_bar = FALSE)

#corr plot
ingredients_df_bin %>% 
  select(contains("bin"), rating) %>%
  plot_correlation()

# # With rating as a factor
# ingredients_df_bin %>% 
#   select(contains("bin"), rating) %>% 
#   mutate(across(rating, as.factor)) %>% 
#   plot_correlation()
# 
# #From this graph we also notice that recipes with rating at 3.75 have slightly positive relationship with carbs and vegetables, whereas recipes with rating at 5 have slightly negative relationship with the same features. We assume then that recipes containing vegetables and carbs tend to be less appreciated.

ingredients_df_bin %>% 
  select(contains("bin"), rating) %>%
  mutate(rating_bin = ifelse(rating>4, "good", "bad"), across(everything(), as.factor)) %>% 
  select(-rating) %>% 
  plot_bar(by = "rating_bin", order_bar = FALSE)

#corr plot
ingredients_df_bin %>% 
  select(contains("bin"), rating) %>%
  mutate(rating_bin = ifelse(rating>4, 1, 0)) %>% 
  select(-rating) %>% 
  plot_correlation()

4.2.3 “Total” engineered ingredients variables

#Analysis which single ingredient is present in most recipes
df <- ingredients_df %>% 
  select(-title, -rating) %>% 
  pivot_longer(-ID, names_to = "ingredient", values_to = "value")


ing_top10 <- df %>% 
  group_by(ingredient) %>% 
  summarise(total = sum(value)) %>% 
  ungroup() %>% 
  arrange(desc(total)) %>% 
  dplyr::slice(1:10)

ing_top10 %>% 
  # mutate(ingredient = fct_rev(ingredient)) %>% 
  ggplot(aes(x=reorder(ingredient, total), y=total, fill=ingredient)) +
  geom_bar(stat = "identity") +
  scale_fill_viridis(discrete = TRUE) +
  scale_x_discrete(guide = guide_axis(n.dodge=2))+
  labs(x = "Ingredient", y = "Value", title = "Total amount of recipes containing each ingredient\nTop 10")

As we can observe, many recipes contain milk cream, onion, tomato, salad, egg and garlic. Some of these are versatile as they can be used for many different kinds of recipes. Onion and garlic are widely used for giving flavour to many dishes, whereas egg and milk cream can be used to cook salty and sweet recipes.

ingredients_df_total %>% 
  select(contains("total"), rating) %>% 
  plot_correlation()

#corr plot
ingredients_df_total %>% 
  select(contains("total"), rating) %>%
  mutate(rating_bin = ifelse(rating>4, 1, 0)) %>% 
  select(-rating) %>% 
  plot_correlation()

#checking some stuff about the new ingredients table
ingredients_df_total %>% 
  select(ID, title, total_ingredients) %>% 
  ggplot(aes(x=total_ingredients)) + 
  geom_bar() + geom_vline(aes(xintercept=mean(total_ingredients)),color="red", linetype="dashed", size=1)+
   scale_x_continuous(breaks = seq(1, 12, by = 1)) +
  labs(x="Number of ingredients per recipe", y = "Recipe Count", title = "Distrubution of number of ingredients per recipe")

#we notice that 117 (no NAs and RAT0, and not duplicated) recipes have 0 ingredients, let's investigate why and how that's possible
ingredients_df_total %>% 
  filter(total_ingredients==0)

#let's pick recipe ID number 1183 which should have poppy and sesame seeds according to the title
recipes %>% 
  filter(ID == 1183) %>% 
  select_if(~ any(. == 1))
#we can see that only 3 variables are equal to 1 here
recipes %>% 
  filter(ID == 365) %>% 
  select_if(~ any(. == 1))

recipes %>% 
  filter(ID == 1089) %>% 
  select_if(~ any(. == 1))

#####
#QUESTION: do we want to keep those recipes?
#####


ingredients_df_total %>% 
  filter(total_ingredients >10)

#eliminating all recipes which do not contain any ingredients that we have classified in categories --> within the "all_ingredients" vector
index_zero_ingredient <- ingredients_df_full %>% 
  filter(total_ingredients == 0) %>% pull(ID)

#removing the 117 recipes with no ingredients listed from recipes and ingredients_df_full
recipes <- recipes %>% 
  filter(!ID %in% index_zero_ingredient)

ingredients_df_full <- ingredients_df_full %>%
  filter(!total_ingredients == 0)

show_nveg <- ingredients_df_full %>%
  filter(vegetables_bin == 1) %>% 
  select(ID, title, total_vegetables) %>% 
  ggplot(aes(x=total_vegetables)) + 
  scale_x_continuous(breaks = seq(1, 9, by = 1)) +
  geom_bar() + geom_vline(aes(xintercept=mean(total_vegetables)),color="blue", linetype="dashed", size=1)


show_nfruit <- ingredients_df_full %>%
  filter(fruits_bin == 1) %>% 
  select(ID, title, total_fruits) %>% 
  ggplot(aes(x=total_fruits)) + 
  scale_x_continuous(breaks = seq(1, 9, by = 1)) +
  geom_bar() + geom_vline(aes(xintercept=mean(total_fruits)),color="blue", linetype="dashed", size=1)


# ingredients_df_full %>% 
#   select(ID, title, total_meat) %>% 
#   ggplot(aes(x=total_meat)) + 
#   geom_bar() + geom_vline(aes(xintercept=mean(total_meat)),color="blue", linetype="dashed", size=1)+
#   labs(x="Number of meats per recipe", y = "Recipe Count", title = "Distrubution of number of meats per recipe")

#let's try to filter by recipes which contain meat to see if my functions work
show_nmeat <- ingredients_df_full %>% 
  filter(meats_bin == 1) %>% 
  select(ID, title, total_meat) %>% 
  ggplot(aes(x=total_meat)) + 
  geom_bar() + geom_vline(aes(xintercept=mean(total_meat)),color="blue", linetype="dashed", size=1)+
  labs(x="Number of meats per recipe", y = "Recipe Count", title = "Distrubution of number of meats per recipe")

#why do we still have value in 0 meats --> it was because when creating the total meat column in ingredients_df_test I did not include the general meat category

grid.arrange(show_nveg, show_nfruit, show_nmeat, ncol=2, nrow =2)

4.3.1 Correlation between nutritional values and engineered ingredients variables

recipes_full %>% 
  select(-ID) %>% 
  plot_correlation()

For instance we notice a positive correlation between proteins and meats_bin which includes all sorts of meat. Another visible positive correlation is the one between sodium and seafood_bin. We might also want to investigate the relationship between calories and carbs_bin.

4.3.2 Barplot and boxplot - Meat and Proteins

# Barplot
barplot1 <- recipes_full %>% 
  ggplot(aes(x = factor(meats_bin), y = protein)) +
  stat_summary(fun = mean, geom = "bar") +
  ggtitle("Average amount of proteins per recipe with and without meat") +
  xlab("Presence of Meat or not") +
  ylab("Protein Content in grams")

# Boxplots per different kinds of meat
recipes_general <- recipes_full %>% 
  select(ID) %>% 
  left_join(recipes, 
           by=c('ID'))

recipes_meat <- recipes_general %>% 
  select(ID, title, rating, calories, protein, fat, sodium, all_of(all_meats))

recipes_meat <- recipes_meat %>% 
  pivot_longer(cols=c("beef", "beef_rib", "beef_shank", "beef_tenderloin", "brisket", "ground_beef", "hamburger", "veal", "bacon", "ham", "pork", "pork_chop", "pork_rib", "pork_tenderloin", "prosciutto", "ground_lamb", "lamb", "lamb_chop", "lamb_shank", "rack_of_lamb", "chicken", "duck", "goose", "poultry", "poultry_sausage", "quail", "turkey", "meatball", "meatloaf", "rabbit", "sausage", "steak", "venison" ),
                    names_to='meats',
                    values_to='yes_or_no') %>% 
  filter(yes_or_no == 1)

multi_boxplot1 <- recipes_meat %>% 
  filter(protein < 450) %>%
  ggplot(aes(x=meats, y=protein, fill=meats)) +
  geom_boxplot(alpha=0.3) +
  scale_y_continuous(breaks=seq(0,7000,25)) +
  coord_flip() +
  ggtitle("Distribution of proteins per recipe according to different kinds of meat") +
  xlab("Meats") +
  ylab("Protein Content in grams") +
  theme(legend.position="none") 

# Here we want to show which kinds of meat specifically have a high level of proteins

grid.arrange(barplot1, multi_boxplot1, ncol=2, nrow =1)

It is very clear that among the recipes with meat, the average content of protein is higher than in recipes without meat. Among those that have meat we notice that goose, venison and lamb shank have the highest content of protein.

4.3.3 Barplot and boxplot - Seafood and Sodium

# Seafood and sodium
barplot2 <- recipes_full %>% 
  ggplot(aes(x = factor(seafood_bin), y = sodium)) +
  stat_summary(fun = mean, geom = "bar") +
  ggtitle("Average amount of sodium per recipe with and without seafood")  +
  xlab("Presence of Seafood or not") +
  ylab("Sodium Content in milligrams")


# Boxplots per different kinds of seafood

recipes_seafood <- recipes_general %>% 
  select(ID, title, rating, calories, protein, fat, sodium, all_of(seafood_vec))

recipes_seafood <- recipes_seafood %>% 
  pivot_longer(cols=c("clam", "crab", "lobster", "mussel", "octopus", "oyster", "scallop", "shellfish", "shrimp", "squid" ),
                    names_to='seafoods',
                    values_to='yes_or_no') %>% 
  filter(yes_or_no == 1)

multi_boxplot2 <- recipes_seafood %>% 
  filter(sodium < 10000) %>%
  ggplot(aes(x=seafoods, y=sodium, fill=seafoods)) +
  geom_boxplot(alpha=0.3) +
  scale_y_continuous(breaks=seq(0,30000,500)) +
  coord_flip() +
  ggtitle("Distribution of sodium per recipe according to different kinds of seafood") +
  xlab("Seafood") +
  ylab("Sodium Content in milligrams") +
  theme(legend.position="none") 

# Here we want to show which kinds of seafood specifically have a high level of sodium

grid.arrange(barplot2, multi_boxplot2, ncol=2, nrow =1)

In this case it is very clear that among the recipes with seafood, the average content of sodium is higher than in recipes without seafood. Among those that have seafood we notice that clams and lobsters have the highest content of sodium.

4.3.4 Barplot and boxplot - Carbs and Calories

# Carbs and calories
barplot3 <- recipes_full %>% 
  ggplot(aes(x = factor(carbs_bin), y = calories)) +
  stat_summary(fun = mean, geom = "bar") +
  ggtitle("Average amount of calories per recipe with and without carbohydrates") +
  xlab("Presence of carbohydrates or not") +
  ylab("Calories content")

# Afterwards we would also want to show which kinds of carbs specifically have a high number of calories


# Boxplots per different kinds of carbs
recipes_carbs <- recipes_general %>% 
  select(ID, title, rating, calories, protein, fat, sodium, all_of(carbs_vec))

recipes_carbs <- recipes_carbs %>% 
  pivot_longer(cols=c("brown_rice", "chickpea", "cornmeal", "couscous", "hominy_cornmeal_masa", "orzo", "pasta", "potato", "rice", "semolina", "sweet_potato_yam", "wild_rice"),
                    names_to='carbs',
                    values_to='yes_or_no') %>% 
  filter(yes_or_no == 1)

multi_boxplot3 <- recipes_carbs %>% 
  filter(sodium < 10000) %>%
  ggplot(aes(x=carbs, y=calories, fill=carbs)) +
  geom_boxplot(alpha=0.3) +
  scale_y_continuous(breaks=seq(0,7000,500)) +
  coord_flip() +
  ggtitle("Distribution of calories per recipe according to different kinds of food high in carbohydrates") +
  xlab("Carbs") +
  ylab("Calories Content") +
  theme(legend.position="none") 

grid.arrange(barplot3, multi_boxplot3, ncol=2, nrow =1)

Recipes which contain carbs register a higher average content of calories than recipes without carbs. Among those that have carbs we notice that pasta and chickpeas are the richest in calories.

4.4.1 Exploratory PCA Analysis

• With only the ones we believe could be useful

nutritional_df <- recipes %>% 
  select(ID, all_of(nutritional_values))

###### CAREFUL --> recipes_analysis should be of dim 10163 x 33
recipes_analysis <- ingredients_df_full %>% 
  left_join(nutritional_df, by="ID") %>% 
  mutate(across(all_of(contains("bin"))), ID = as.character(ID)) %>% 
  select(rating, all_of(nutritional_values), contains("bin"), contains("total"))

recipes_pca2 <- PCA(recipes_analysis, ncp = 33, graph = FALSE)

recipes_pca2

#> **Results for the Principal Component Analysis (PCA)**
#> The analysis was performed on 10163 individuals, described by 33 variables
#> *The results are available in the following objects:
#> 
#>    name               description                          
#> 1  "$eig"             "eigenvalues"                        
#> 2  "$var"             "results for the variables"          
#> 3  "$var$coord"       "coord. for the variables"           
#> 4  "$var$cor"         "correlations variables - dimensions"
#> 5  "$var$cos2"        "cos2 for the variables"             
#> 6  "$var$contrib"     "contributions of the variables"     
#> 7  "$ind"             "results for the individuals"        
#> 8  "$ind$coord"       "coord. for the individuals"         
#> 9  "$ind$cos2"        "cos2 for the individuals"           
#> 10 "$ind$contrib"     "contributions of the individuals"   
#> 11 "$call"            "summary statistics"                 
#> 12 "$call$centre"     "mean of the variables"              
#> 13 "$call$ecart.type" "standard error of the variables"    
#> 14 "$call$row.w"      "weights for the individuals"        
#> 15 "$call$col.w"      "weights for the variables"

fviz_pca_var(recipes_pca2)

fviz_contrib(recipes_pca2, choice = "var", axes = 1)

fviz_contrib(recipes_pca2, choice = "var", axes = 2)

fviz_pca_biplot(recipes_pca2) ## biplot

fviz_eig(recipes_pca2, addlabels = TRUE, ncp=11)

p1 <- fviz_pca_biplot(recipes_pca2, axes = 1:2) 
p2 <- fviz_pca_biplot(recipes_pca2, axes = 3:4) 
p3 <- fviz_pca_biplot(recipes_pca2, axes = 5:6) 
p4 <- fviz_pca_biplot(recipes_pca2, axes = 7:8) 
p5 <- fviz_pca_biplot(recipes_pca2, axes = 9:10) 

grid.arrange(p1, p2, p3, p4, p5, nrow = 3, ncol=2)

recipe_hc2 <- hclust(dist(recipes_analysis, method = "manhattan"))

recipe_clust2 <- cutree(recipe_hc2, k = 10)

fviz_pca_biplot(recipes_pca2,
             col.ind = factor(recipe_clust2))

4.5.1 Seasons

#Create seasons df
seasons_df <- recipes %>% 
  select(ID, rating, all_of(seasons_vec)) %>% 
  filter(if_any(all_of(seasons_vec)) == 1) %>% 
  mutate(sum_season = rowSums(across(all_of(seasons_vec))))

seasons_df %>% 
ggplot(aes(x=sum_season)) +
  geom_bar()

seasons_df %>% 
  filter(sum_season==3)

#>       ID rating winter spring summer fall sum_season
#> 1   1271  4.375      0      1      1    1          3
#> 2   1430  4.375      1      1      0    1          3
#> 3   2672  4.375      0      1      1    1          3
#> 4   2917  3.750      1      1      0    1          3
#> 5   4180  4.375      1      1      0    1          3
#> 6   7740  4.375      1      1      0    1          3
#> 7   8045  4.375      0      1      1    1          3
#> 8  10782  4.375      0      1      1    1          3
#> 9  12421  4.375      1      1      0    1          3
#> 10 12545  5.000      1      1      1    0          3
#> 11 15494  4.375      1      0      1    1          3
#> 12 16603  3.750      1      0      1    1          3
#> 13 16729  4.375      0      1      1    1          3
#> 14 17102  3.750      1      1      0    1          3
#> 15 18603  4.375      1      1      0    1          3
#> 16 18854  5.000      1      1      0    1          3
#> 17 18908  5.000      1      1      1    0          3
#> 18 19913  3.750      1      0      1    1          3

seasons_df %>% 
  filter(sum_season==4)

#>       ID rating winter spring summer fall sum_season
#> 1     54  5.000      1      1      1    1          4
#> 2   1837  3.750      1      1      1    1          4
#> 3   4733  3.125      1      1      1    1          4
#> 4   4980  3.750      1      1      1    1          4
#> 5   7341  1.250      1      1      1    1          4
#> 6   8593  5.000      1      1      1    1          4
#> 7  13759  4.375      1      1      1    1          4
#> 8  14419  3.750      1      1      1    1          4
#> 9  16448  2.500      1      1      1    1          4
#> 10 19011  3.750      1      1      1    1          4

#total of 29 recipes with either 3 or 4 --> let's discard them

#let's look a bit more closely to those with 2 seasons to see if they are next to each other or not

seasons_df %>% 
  filter(sum_season==2)

#>        ID rating winter spring summer fall sum_season
#> 1      25  3.750      1      0      0    1          2
#> 2      27  3.750      0      1      1    0          2
#> 3      57  4.375      1      0      0    1          2
#> 4      67  3.125      1      0      0    1          2
#> 5     130  4.375      1      0      0    1          2
#> 6     135  3.750      1      0      0    1          2
#> 7     153  4.375      0      0      1    1          2
#> 8     156  4.375      1      0      0    1          2
#> 9     167  4.375      1      0      0    1          2
#> 10    179  4.375      1      0      0    1          2
#> 11    238  3.750      0      0      1    1          2
#> 12    256  3.750      1      0      0    1          2
#> 13    275  3.750      0      1      1    0          2
#> 14    278  4.375      0      1      1    0          2
#> 15    368  4.375      1      0      0    1          2
#> 16    369  4.375      0      1      1    0          2
#> 17    401  3.750      1      0      0    1          2
#> 18    449  3.750      0      0      1    1          2
#> 19    501  4.375      0      1      1    0          2
#> 20    516  3.125      1      0      0    1          2
#> 21    538  5.000      1      0      0    1          2
#> 22    543  3.125      0      1      1    0          2
#> 23    558  4.375      1      0      0    1          2
#> 24    597  4.375      1      0      0    1          2
#> 25    599  4.375      1      0      0    1          2
#> 26    614  4.375      1      1      0    0          2
#> 27    618  4.375      1      0      0    1          2
#> 28    639  3.750      1      0      0    1          2
#> 29    664  3.750      1      0      0    1          2
#> 30    666  5.000      1      0      0    1          2
#> 31    682  4.375      1      1      0    0          2
#> 32    697  5.000      0      1      1    0          2
#> 33    700  4.375      0      1      1    0          2
#> 34    738  3.750      1      0      0    1          2
#> 35    802  3.750      0      0      1    1          2
#> 36    830  3.750      1      0      0    1          2
#> 37    864  5.000      1      0      0    1          2
#> 38    866  4.375      1      0      0    1          2
#> 39    890  3.125      1      0      0    1          2
#> 40    900  4.375      1      0      0    1          2
#> 41    902  4.375      1      0      0    1          2
#> 42    903  3.750      1      0      0    1          2
#> 43    917  4.375      1      0      0    1          2
#> 44    920  2.500      0      1      1    0          2
#> 45    956  4.375      1      0      0    1          2
#> 46    964  4.375      0      1      1    0          2
#> 47    986  4.375      1      0      0    1          2
#> 48   1003  4.375      1      1      0    0          2
#> 49   1060  4.375      1      0      0    1          2
#> 50   1106  4.375      0      1      1    0          2
#> 51   1134  4.375      1      0      0    1          2
#> 52   1179  3.125      1      0      0    1          2
#> 53   1207  4.375      0      1      1    0          2
#> 54   1212  4.375      0      1      1    0          2
#> 55   1268  4.375      0      1      1    0          2
#> 56   1275  3.750      0      1      1    0          2
#> 57   1290  4.375      1      0      0    1          2
#> 58   1308  3.125      0      0      1    1          2
#> 59   1345  4.375      0      0      1    1          2
#> 60   1346  3.125      1      0      0    1          2
#> 61   1405  5.000      1      0      0    1          2
#> 62   1406  3.750      1      0      0    1          2
#> 63   1411  4.375      1      0      0    1          2
#> 64   1459  3.750      1      0      0    1          2
#> 65   1507  4.375      0      1      1    0          2
#> 66   1528  4.375      0      1      1    0          2
#> 67   1581  5.000      1      0      0    1          2
#> 68   1602  5.000      1      1      0    0          2
#> 69   1648  3.750      0      1      1    0          2
#> 70   1688  3.125      0      1      0    1          2
#> 71   1732  3.750      0      0      1    1          2
#> 72   1744  3.750      1      0      0    1          2
#> 73   1757  3.750      1      0      0    1          2
#> 74   1794  5.000      1      1      0    0          2
#> 75   1797  3.125      1      0      0    1          2
#> 76   1805  4.375      0      1      1    0          2
#> 77   1806  4.375      1      1      0    0          2
#> 78   1832  3.750      1      0      0    1          2
#> 79   1846  5.000      1      0      0    1          2
#> 80   1895  3.750      1      0      0    1          2
#> 81   1932  4.375      1      0      0    1          2
#> 82   1940  4.375      1      0      0    1          2
#> 83   2020  4.375      0      1      1    0          2
#> 84   2035  5.000      0      1      1    0          2
#> 85   2069  5.000      1      0      0    1          2
#> 86   2088  4.375      0      1      1    0          2
#> 87   2093  4.375      1      0      0    1          2
#> 88   2117  4.375      1      0      0    1          2
#> 89   2137  4.375      1      0      0    1          2
#> 90   2207  4.375      0      0      1    1          2
#> 91   2241  3.750      1      0      0    1          2
#> 92   2243  5.000      1      0      0    1          2
#> 93   2245  4.375      1      0      0    1          2
#> 94   2261  5.000      0      1      1    0          2
#> 95   2269  4.375      1      0      0    1          2
#> 96   2328  4.375      1      0      0    1          2
#> 97   2331  4.375      1      0      0    1          2
#> 98   2380  3.750      1      0      0    1          2
#> 99   2417  3.750      0      1      1    0          2
#> 100  2518  3.750      1      0      0    1          2
#> 101  2610  3.750      0      1      1    0          2
#> 102  2620  4.375      1      0      0    1          2
#> 103  2694  3.125      1      0      0    1          2
#> 104  2717  4.375      1      0      0    1          2
#> 105  2727  5.000      0      0      1    1          2
#> 106  2733  3.750      1      0      0    1          2
#> 107  2746  5.000      0      1      1    0          2
#> 108  2756  3.125      1      0      0    1          2
#> 109  2769  4.375      1      0      0    1          2
#> 110  2778  4.375      0      1      1    0          2
#> 111  2825  5.000      1      0      0    1          2
#> 112  2835  3.750      1      0      0    1          2
#> 113  2838  3.750      0      1      1    0          2
#> 114  2842  3.750      1      0      0    1          2
#> 115  2898  3.750      1      0      0    1          2
#> 116  2938  4.375      0      1      1    0          2
#> 117  2952  4.375      0      1      1    0          2
#> 118  2963  5.000      1      0      0    1          2
#> 119  2965  5.000      1      1      0    0          2
#> 120  2966  3.750      1      0      0    1          2
#> 121  3007  3.125      1      0      0    1          2
#> 122  3010  4.375      0      1      0    1          2
#> 123  3049  4.375      1      0      0    1          2
#> 124  3076  4.375      1      0      0    1          2
#> 125  3149  4.375      0      1      1    0          2
#> 126  3172  3.750      1      0      0    1          2
#> 127  3212  4.375      1      0      0    1          2
#> 128  3219  3.750      0      1      1    0          2
#> 129  3233  3.750      1      0      0    1          2
#> 130  3238  5.000      0      1      1    0          2
#> 131  3257  5.000      1      0      0    1          2
#> 132  3310  4.375      1      0      0    1          2
#> 133  3369  4.375      1      0      0    1          2
#> 134  3402  3.750      1      0      0    1          2
#> 135  3406  4.375      1      0      0    1          2
#> 136  3417  4.375      0      1      1    0          2
#> 137  3468  3.125      0      1      1    0          2
#> 138  3548  4.375      1      0      0    1          2
#> 139  3562  4.375      1      0      0    1          2
#> 140  3569  3.750      1      0      0    1          2
#> 141  3600  5.000      1      0      0    1          2
#> 142  3618  5.000      0      1      1    0          2
#> 143  3663  4.375      1      0      0    1          2
#> 144  3698  4.375      1      0      0    1          2
#> 145  3734  4.375      1      0      1    0          2
#> 146  3773  3.750      1      0      0    1          2
#> 147  3881  4.375      0      1      1    0          2
#> 148  3926  4.375      1      0      0    1          2
#> 149  3945  4.375      1      0      0    1          2
#> 150  3985  4.375      1      0      0    1          2
#> 151  4016  3.750      0      1      1    0          2
#> 152  4025  4.375      1      0      0    1          2
#> 153  4040  4.375      0      1      1    0          2
#> 154  4056  4.375      0      1      1    0          2
#> 155  4064  4.375      1      0      0    1          2
#> 156  4074  4.375      0      1      0    1          2
#> 157  4195  4.375      0      1      1    0          2
#> 158  4204  4.375      1      0      0    1          2
#> 159  4241  5.000      0      1      0    1          2
#> 160  4377  4.375      1      0      0    1          2
#> 161  4414  3.125      1      0      0    1          2
#> 162  4473  4.375      1      0      0    1          2
#> 163  4510  4.375      0      0      1    1          2
#> 164  4539  4.375      1      0      0    1          2
#> 165  4552  4.375      1      0      0    1          2
#> 166  4637  4.375      1      0      0    1          2
#> 167  4682  4.375      1      0      0    1          2
#> 168  4737  4.375      1      0      0    1          2
#> 169  4788  4.375      1      0      0    1          2
#> 170  4839  4.375      1      0      0    1          2
#> 171  4887  3.750      1      0      0    1          2
#> 172  4946  4.375      1      0      0    1          2
#> 173  4966  4.375      0      1      1    0          2
#> 174  5149  5.000      0      1      1    0          2
#> 175  5151  4.375      1      0      0    1          2
#> 176  5216  3.750      1      0      0    1          2
#> 177  5235  4.375      0      1      1    0          2
#> 178  5373  4.375      1      0      0    1          2
#> 179  5407  1.875      1      0      0    1          2
#> 180  5410  5.000      1      0      1    0          2
#> 181  5450  3.750      1      0      0    1          2
#> 182  5451  4.375      0      1      1    0          2
#> 183  5485  4.375      0      1      1    0          2
#> 184  5516  3.750      1      1      0    0          2
#> 185  5537  2.500      0      1      1    0          2
#> 186  5597  4.375      1      0      0    1          2
#> 187  5613  3.125      0      0      1    1          2
#> 188  5622  3.750      1      0      0    1          2
#> 189  5655  4.375      1      0      0    1          2
#> 190  5660  4.375      1      1      0    0          2
#> 191  5689  4.375      1      0      0    1          2
#> 192  5757  4.375      0      0      1    1          2
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#> 572 18327  4.375      1      0      0    1          2
#> 573 18446  4.375      1      0      1    0          2
#> 574 18530  3.750      1      0      0    1          2
#> 575 18602  4.375      0      1      1    0          2
#> 576 18825  4.375      1      0      0    1          2
#> 577 18832  3.750      1      0      0    1          2
#> 578 18837  5.000      1      0      0    1          2
#> 579 18852  4.375      1      0      0    1          2
#> 580 18885  4.375      1      0      0    1          2
#> 581 18982  3.750      0      1      1    0          2
#> 582 19108  3.125      1      0      0    1          2
#> 583 19117  3.125      1      0      0    1          2
#> 584 19205  5.000      1      0      0    1          2
#> 585 19273  4.375      1      0      0    1          2
#> 586 19329  4.375      0      1      1    0          2
#> 587 19338  3.750      1      0      0    1          2
#> 588 19369  4.375      0      1      1    0          2
#> 589 19399  3.750      1      0      0    1          2
#> 590 19493  3.750      0      1      1    0          2
#> 591 19539  4.375      0      1      1    0          2
#> 592 19547  3.750      1      0      0    1          2
#> 593 19563  4.375      1      0      0    1          2
#> 594 19615  4.375      1      0      0    1          2
#> 595 19625  4.375      1      0      0    1          2
#> 596 19627  3.750      1      0      0    1          2
#> 597 19643  3.125      0      0      1    1          2
#> 598 19685  4.375      1      0      0    1          2
#> 599 19792  3.750      0      1      1    0          2
#> 600 19802  4.375      1      0      0    1          2
#> 601 19815  4.375      1      0      0    1          2
#> 602 19881  4.375      0      1      1    0          2
#> 603 19889  4.375      1      0      0    1          2
#> 604 19905  5.000      0      1      1    0          2
#> 605 20041  4.375      1      0      0    1          2
#> 606 20049  4.375      0      1      1    0          2

### should we keep those observations???

As we can see, there is again no correlation between seasons and recipe ratings.

seasons_df %>% 
  select(-sum_season, -ID) %>% 
  plot_correlation()

CAN TRY TO feature engineer rating above 4

Inconclusive result, again.

seasons_df <-seasons_df %>% 
  mutate(rating_above_4 = ifelse(rating > 4, 1, 0), rating_5 = ifelse(rating == 5, 1, 0), rating_1.25 = ifelse(rating == 1.25, 1, 0))

seasons_df %>% 
  select(rating, rating_above_4, all_of(seasons_vec))%>% 
  plot_correlation()

seasons_df %>%
  select(rating_5, rating_1.25, all_of(seasons_vec)) %>%
  plot_correlation()

4.5.2 Recipe Type

#TO ADD WHEN COMPLETED

#taking into account only the "main" recipe types
recipe_types_select <- c("breakfast", "brunch", "dessert", "dinner", "lunch")

type_df <- recipes %>% 
  select(ID, rating, all_of(recipe_types_select)) %>% 
  filter(if_any(all_of(recipe_types_select)) == 1) %>% 
  mutate(sum_type= rowSums(across(all_of(recipe_types_select))))

type_df %>% 
  ggplot(aes(x=sum_type)) +
  geom_bar()

# type_df %>% 
#   filter(sum_type == 2)

# left with 3333 obs after filtering
type_df <- type_df %>% 
  filter(!sum_type >1)

Once again very low correlation for recipe types, we will not included them in the analysis.

type_df %>% 
  select(-c(ID, sum_type)) %>% 
  plot_correlation()

4.5.3 Countries

Only 54 recipes containing info about the country so we can’t use it either for the analysis.

countries_df <- recipes %>% 
  select(ID, rating, all_of(countries)) %>% 
  filter(if_any(all_of(countries)) == 1) %>% 
  mutate(sum_type= rowSums(across(all_of(countries))))

countries_df %>% 
  ggplot(aes(x=sum_type)) +
  geom_bar()

5.1.1 Creating train and test sets for some variable combination

#for train multi
tr_multi_all <- train_multi
te_multi_all <- test_multi

tr_multi_Nut <- train_multi %>% 
  select(rating, all_of(nutritional_values))
te_multi_Nut <- test_multi %>% 
  select(rating, all_of(nutritional_values))

5.1.2 TrainControl Functions

Here we create the train control functions we will use throughout the project.

#creating train control data for unbalanced data
trCtrl <- trainControl(method = "cv",
                       number = 5)

#train control with downsampling
trCtrl_down <- trainControl(method = "cv",
                       number = 5,
                       sampling = "down")

#train control with downsampling twoclass summary
trCtrl_down_twoClass <- trainControl(method = "cv",
                       summaryFunction = twoClassSummary,
                       classProbs = TRUE,
                       number = 5,
                       sampling = "down"
                       )

5.2.1 Fitting RF - multi_all

Hyperparameters

Best tune: mtry = 2

Accuracy metrics

• ACC 45.6
• Kappa 0.002

set.seed(12)
rf_multi_all_fit <- caret::train(rating ~ .,
                     data = tr_multi_all,
                     method = "rf",
                     preProcess = NULL,
                     trControl = trCtrl,
                     tuneLength = 3)
#show the random forest with cv 
rf_multi_all_fit

#> Random Forest 
#> 
#> 7624 samples
#>   32 predictor
#>    7 classes: '1.25', '1.875', '2.5', '3.125', '3.75', '4.375', '5' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6100, 6100, 6098, 6099, 6099 
#> Resampling results across tuning parameters:
#> 
#>   mtry  Accuracy  Kappa   
#>    2    0.4568    0.003999
#>   17    0.4343    0.050215
#>   32    0.4332    0.050089
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was mtry = 2.

plot(rf_multi_all_fit, main = "Plot of CV Accuracy relative to Mtry parameter")

5.2.2 Predictions RF - multi_all

As can be seen by the predictions below, our assumptions were valid. The model does a really bad job at classifying the test set into the correct rating categories. It is equivalent to a random model with a very strong bias towards the majority class at 4.375 (due to the data imbalance present in the rating variable.)

#make predictions
rf_multi_all_pred <- predict(rf_multi_all_fit, newdata = test_multi)

#confusion matrix 
confusionMatrix(data = rf_multi_all_pred, reference = test_multi$rating)

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction 1.25 1.875  2.5 3.125 3.75 4.375    5
#>      1.25     0     0    0     0    0     0    0
#>      1.875    0     0    0     0    0     0    0
#>      2.5      0     0    0     0    0     0    0
#>      3.125    0     0    0     0    0     0    0
#>      3.75     2     1    1     4    5     7    5
#>      4.375   19    11   67   204  724  1151  337
#>      5        0     0    0     0    0     1    0
#> 
#> Overall Statistics
#>                                         
#>                Accuracy : 0.455         
#>                  95% CI : (0.436, 0.475)
#>     No Information Rate : 0.456         
#>     P-Value [Acc > NIR] : 0.555         
#>                                         
#>                   Kappa : 0.001         
#>                                         
#>  Mcnemar's Test P-Value : NA            
#> 
#> Statistics by Class:
#> 
#>                      Class: 1.25 Class: 1.875 Class: 2.5
#> Sensitivity              0.00000      0.00000     0.0000
#> Specificity              1.00000      1.00000     1.0000
#> Pos Pred Value               NaN          NaN        NaN
#> Neg Pred Value           0.99173      0.99527     0.9732
#> Prevalence               0.00827      0.00473     0.0268
#> Detection Rate           0.00000      0.00000     0.0000
#> Detection Prevalence     0.00000      0.00000     0.0000
#> Balanced Accuracy        0.50000      0.50000     0.5000
#>                      Class: 3.125 Class: 3.75 Class: 4.375 Class: 5
#> Sensitivity                0.0000     0.00686        0.993 0.000000
#> Specificity                1.0000     0.98895        0.013 0.999545
#> Pos Pred Value                NaN     0.20000        0.458 0.000000
#> Neg Pred Value             0.9181     0.71201        0.692 0.865248
#> Prevalence                 0.0819     0.28712        0.456 0.134699
#> Detection Rate             0.0000     0.00197        0.453 0.000000
#> Detection Prevalence       0.0000     0.00985        0.990 0.000394
#> Balanced Accuracy          0.5000     0.49790        0.503 0.499772

5.2.3 Fitting - RF multi_Nut

We now try another RF but only with the nutritional values as explanatory variables to see if it changes something.

Hyperparameters

Best tune: mtry = 2

Accuracy metrics

• ACC 41.6
• Kappa 0.048

set.seed(12)
rf_multi_Nut_fit <- train(rating ~ .,
                     data = tr_multi_Nut,
                     method = "rf",
                     preProcess = NULL,
                     trControl = trCtrl,
                     tuneLength = 3)
#show the random forest with cv 
rf_multi_Nut_fit

#> Random Forest 
#> 
#> 7624 samples
#>    4 predictor
#>    7 classes: '1.25', '1.875', '2.5', '3.125', '3.75', '4.375', '5' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6100, 6100, 6098, 6099, 6099 
#> Resampling results across tuning parameters:
#> 
#>   mtry  Accuracy  Kappa  
#>   2     0.4122    0.03741
#>   3     0.4073    0.03377
#>   4     0.4083    0.03771
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was mtry = 2.

plot(rf_multi_Nut_fit, main = "Plot of CV Accuracy relative to Mtry parameter")

5.2.4 Predictions - RF multi_Nut

As can be seen by the predictions below, our assumptions were valid. The model does a really bad job at classifying the test set into the correct rating categories. It is equivalent to a random model with a very strong bias towards the majority class at 4.375 (due to the data imbalance present in the rating variable.)

#make predictions
rf_multi_Nut_pred <- predict(rf_multi_Nut_fit, newdata = te_multi_all)

#confusion matrix 
confusionMatrix(data = rf_multi_Nut_pred, reference = te_multi_Nut$rating)

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction 1.25 1.875 2.5 3.125 3.75 4.375   5
#>      1.25     0     0   0     0    0     0   0
#>      1.875    0     0   0     0    0     0   0
#>      2.5      0     0   0     0    2     5   0
#>      3.125    0     0   1     7   12    15   8
#>      3.75     4     6  13    53  184   264  72
#>      4.375   15     5  44   134  496   815 209
#>      5        2     1  10    14   35    60  53
#> 
#> Overall Statistics
#>                                         
#>                Accuracy : 0.417         
#>                  95% CI : (0.398, 0.437)
#>     No Information Rate : 0.456         
#>     P-Value [Acc > NIR] : 1             
#>                                         
#>                   Kappa : 0.049         
#>                                         
#>  Mcnemar's Test P-Value : NA            
#> 
#> Statistics by Class:
#> 
#>                      Class: 1.25 Class: 1.875 Class: 2.5
#> Sensitivity              0.00000      0.00000    0.00000
#> Specificity              1.00000      1.00000    0.99717
#> Pos Pred Value               NaN          NaN    0.00000
#> Neg Pred Value           0.99173      0.99527    0.97314
#> Prevalence               0.00827      0.00473    0.02678
#> Detection Rate           0.00000      0.00000    0.00000
#> Detection Prevalence     0.00000      0.00000    0.00276
#> Balanced Accuracy        0.50000      0.50000    0.49858
#>                      Class: 3.125 Class: 3.75 Class: 4.375 Class: 5
#> Sensitivity               0.03365      0.2524        0.703   0.1550
#> Specificity               0.98456      0.7724        0.346   0.9445
#> Pos Pred Value            0.16279      0.3087        0.474   0.3029
#> Neg Pred Value            0.91947      0.7195        0.581   0.8777
#> Prevalence                0.08192      0.2871        0.456   0.1347
#> Detection Rate            0.00276      0.0725        0.321   0.0209
#> Detection Prevalence      0.01694      0.2347        0.677   0.0689
#> Balanced Accuracy         0.50910      0.5124        0.524   0.5497

5.2.5 Evaluation and decision for rest of analysis

Since we see a huge bias towards the majority class in unbalanced data (which we expected), we have to take a decision between 3 options:

• We could try balancing the 7 levels, either up or down. Due to the very large disparity in observation counts per level (min at 32 and max at 3481), we believe than neither up- nor downsampling would be ideal. Indeed, upsampling would mean creating a massive amount of artificial observations through replacement for the minority classes, while downsampling would leave us with an insufficient total amount of observations.
• We could try to aggregate the minority classes into one single class (i.e., putting 1.25, 1.875, 2.5, and 3.125 together), leaving us with 4 final classes. There would still be a significant imbalance however, and given the near-random classification that we observed above, we do not believe aggregating those classes is the solution.
• We could transform the 7 levels into a binary classification problem. This would help both with class imbalance and would hopefully also lead to higher accuracy metrics by simplifying the classification task.

After careful reflection, we believe that the 3rd options is our best bet. We therefore transform the 7-level rating variable into a binary rating variable, with the threshold at 4. This means that all ratings below 4 are now considered as “bad” and all ratings above 4 are considered as “good”.

5.3.1 Data preparation for analysis

#creating binary rating variable
recipes_analysis_bin <- recipes_analysis %>% 
  mutate(rating_bin = as.factor(ifelse(rating<4, "bad", "good"))) %>% 
  select(-rating)

#reversing rating_bin factor order
recipes_analysis_bin$rating_bin <- factor(recipes_analysis_bin$rating_bin, levels=rev(levels(recipes_analysis_bin$rating_bin )))

#normalising newly created df
recipes_analysis_bin <- recipes_analysis_bin %>% 
  mutate(across(where(is.numeric), my_normalise))

#creating training and test sets
set.seed(12)
index_bin <- createDataPartition(recipes_analysis_bin$rating_bin, p=0.75, list = FALSE)

#creating training and test set with multilevel rating variable
train_bin <- recipes_analysis_bin[index_bin, ]
test_bin <- recipes_analysis_bin[-index_bin, ]

table(train_bin$rating_bin)

#> 
#> good  bad 
#> 4508 3115

#creating train and test set for all combinations of variables, for binary rating df
train_bin_Nut <- train_bin %>% 
  select(rating_bin, all_of(nutritional_values))
test_bin_Nut <- test_bin %>% 
  select(rating_bin, all_of(nutritional_values))

train_bin_NuTo <- train_bin %>% 
  select(rating_bin, all_of(nutritional_values), all_of(contains("total")))
test_bin_NuTo <- test_bin %>% 
  select(rating_bin, all_of(nutritional_values), all_of(contains("total")))

train_bin_NuBi <- train_bin %>% 
  select(rating_bin, all_of(nutritional_values), all_of(contains("bin")))
test_bin_NuBi <- test_bin %>% 
  select(rating_bin, all_of(nutritional_values), all_of(contains("bin")))

train_bin_Tot <- train_bin %>% 
  select(rating_bin, all_of(contains("total")))
test_bin_Tot <- test_bin %>% 
  select(rating_bin, all_of(contains("total")))

train_bin_Bin <- train_bin %>% 
  select(rating_bin, all_of(contains("bin")))
test_bin_Bin <- test_bin %>% 
  select(rating_bin, all_of(contains("bin")))

5.3.2 Logistic Regression - unbalanced - Nut

set.seed(12)
logr_Nut_unbal_fit <- caret::train(rating_bin ~.,
                data = train_bin_Nut,
                method = "glm",
                family = "binomial",
                trControl = trCtrl)
logr_Nut_unbal_fit

#> Generalized Linear Model 
#> 
#> 7623 samples
#>    4 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results:
#> 
#>   Accuracy  Kappa
#>   0.5914    0

logr_Nut_unbal_pred <- predict(logr_Nut_unbal_fit, newdata = test_bin_Nut, type = "raw")

CM <- confusionMatrix(reference = test_bin_Nut$rating_bin, data = logr_Nut_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1502 1038
#>       bad     0    0
#>                                         
#>                Accuracy : 0.591         
#>                  95% CI : (0.572, 0.611)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.509         
#>                                         
#>                   Kappa : 0             
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 1.000         
#>             Specificity : 0.000         
#>          Pos Pred Value : 0.591         
#>          Neg Pred Value :   NaN         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.591         
#>    Detection Prevalence : 1.000         
#>       Balanced Accuracy : 0.500         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, LogReg_Nut = summary_table_fun(CM))

5.3.3 Logistic Regression - unbalanced - NuBi

set.seed(12)
logr_NuBi_unbal_fit <- train(rating_bin ~.,
                data = train_bin_NuBi,
                method = "glm",
                family = "binomial",
                trControl = trCtrl)
logr_NuBi_unbal_fit

#> Generalized Linear Model 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results:
#> 
#>   Accuracy  Kappa  
#>   0.5971    0.04562

logr_NuBi_unbal_pred <- predict(logr_NuBi_unbal_fit, newdata = test_bin_NuBi, type = "raw")

CM <- confusionMatrix(reference = test_bin_NuBi$rating_bin, data = logr_NuBi_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1399  950
#>       bad   103   88
#>                                         
#>                Accuracy : 0.585         
#>                  95% CI : (0.566, 0.605)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.734         
#>                                         
#>                   Kappa : 0.019         
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 0.9314        
#>             Specificity : 0.0848        
#>          Pos Pred Value : 0.5956        
#>          Neg Pred Value : 0.4607        
#>              Prevalence : 0.5913        
#>          Detection Rate : 0.5508        
#>    Detection Prevalence : 0.9248        
#>       Balanced Accuracy : 0.5081        
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, LogReg_NuBi = summary_table_fun(CM))

5.3.4 Logistic Regression - unbalanced - NuTo

set.seed(12)
logr_NuTo_unbal_fit <- train(rating_bin ~.,
                data = train_bin_NuTo,
                method = "glm",
                family = "binomial",
                trControl = trCtrl)
logr_NuTo_unbal_fit

#> Generalized Linear Model 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results:
#> 
#>   Accuracy  Kappa  
#>   0.595     0.03911

logr_NuTo_unbal_pred <- predict(logr_NuTo_unbal_fit, newdata = test_bin_NuTo, type = "raw")

CM <- confusionMatrix(reference = test_bin_NuTo$rating_bin, data = logr_NuTo_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1401  942
#>       bad   101   96
#>                                        
#>                Accuracy : 0.589        
#>                  95% CI : (0.57, 0.609)
#>     No Information Rate : 0.591        
#>     P-Value [Acc > NIR] : 0.588        
#>                                        
#>                   Kappa : 0.029        
#>                                        
#>  Mcnemar's Test P-Value : <2e-16       
#>                                        
#>             Sensitivity : 0.9328       
#>             Specificity : 0.0925       
#>          Pos Pred Value : 0.5980       
#>          Neg Pred Value : 0.4873       
#>              Prevalence : 0.5913       
#>          Detection Rate : 0.5516       
#>    Detection Prevalence : 0.9224       
#>       Balanced Accuracy : 0.5126       
#>                                        
#>        'Positive' Class : good         
#> 

summary_table_unbal <- cbind(summary_table_unbal, LogReg_NuTo = summary_table_fun(CM))

5.3.5 KNN - unbalanced - Nut

set.seed(12)
knn_Nut_unbal_fit <- caret::train(rating_bin ~.,
                data = train_bin_Nut,
                method = "knn",
                trControl = trCtrl,
                tuneGrid= data.frame(k = seq(105, 115,by = 2))#initially checked on 1-151 range, best was 111
                )
knn_Nut_unbal_fit

#> k-Nearest Neighbors 
#> 
#> 7623 samples
#>    4 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   k    Accuracy  Kappa  
#>   105  0.5890    0.03661
#>   107  0.5876    0.03221
#>   109  0.5881    0.03268
#>   111  0.5885    0.03322
#>   113  0.5895    0.03570
#>   115  0.5881    0.03235
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was k = 113.

knn_Nut_unbal_pred <- predict(knn_Nut_unbal_fit, newdata = test_bin_Nut, type = "raw")

CM <- confusionMatrix(reference = test_bin_Nut$rating_bin, data = knn_Nut_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1382  903
#>       bad   120  135
#>                                         
#>                Accuracy : 0.597         
#>                  95% CI : (0.578, 0.616)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.279         
#>                                         
#>                   Kappa : 0.057         
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 0.920         
#>             Specificity : 0.130         
#>          Pos Pred Value : 0.605         
#>          Neg Pred Value : 0.529         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.544         
#>    Detection Prevalence : 0.900         
#>       Balanced Accuracy : 0.525         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, KNN_Nut = summary_table_fun(CM))

5.3.6 KNN - unbalanced - NuBi

set.seed(12)
knn_NuBi_unbal_fit <- caret::train(rating_bin ~.,
                data = train_bin_NuBi,
                method = "knn",
                trControl = trCtrl,
                tuneGrid= data.frame(k = seq(131, 141,by = 2))#initially checked on 1-151 range, best was 135
                )
knn_NuBi_unbal_fit

#> k-Nearest Neighbors 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   k    Accuracy  Kappa  
#>   131  0.5954    0.04616
#>   133  0.5936    0.04216
#>   135  0.5935    0.04255
#>   137  0.5946    0.04432
#>   139  0.5948    0.04454
#>   141  0.5943    0.04332
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was k = 131.

knn_NuBi_unbal_pred <- predict(knn_NuBi_unbal_fit, newdata = test_bin_NuBi, type = "raw")

CM <- confusionMatrix(reference = test_bin_NuBi$rating_bin, data = knn_NuBi_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1353  908
#>       bad   149  130
#>                                         
#>                Accuracy : 0.584         
#>                  95% CI : (0.564, 0.603)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.785         
#>                                         
#>                   Kappa : 0.029         
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 0.901         
#>             Specificity : 0.125         
#>          Pos Pred Value : 0.598         
#>          Neg Pred Value : 0.466         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.533         
#>    Detection Prevalence : 0.890         
#>       Balanced Accuracy : 0.513         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, KNN_NuBi = summary_table_fun(CM))

5.3.7 KNN - unbalanced - NuTo

set.seed(12)
knn_NuTo_unbal_fit <- caret::train(rating_bin ~.,
                data = train_bin_NuTo,
                method = "knn",
                trControl = trCtrl,
                tuneGrid= data.frame(k = seq(131, 141,by = 2))#initially checked on 1-151 range, best was 135
                )
knn_NuTo_unbal_fit

#> k-Nearest Neighbors 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   k    Accuracy  Kappa  
#>   131  0.5907    0.03996
#>   133  0.5920    0.04324
#>   135  0.5925    0.04351
#>   137  0.5931    0.04508
#>   139  0.5929    0.04538
#>   141  0.5928    0.04556
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was k = 137.

knn_NuTo_unbal_pred <- predict(knn_NuTo_unbal_fit, newdata = test_bin_NuTo, type = "raw")

CM <- confusionMatrix(reference = test_bin_NuTo$rating_bin, data = knn_NuTo_unbal_pred, positive="good")
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1359  910
#>       bad   143  128
#>                                         
#>                Accuracy : 0.585         
#>                  95% CI : (0.566, 0.605)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.734         
#>                                         
#>                   Kappa : 0.032         
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 0.905         
#>             Specificity : 0.123         
#>          Pos Pred Value : 0.599         
#>          Neg Pred Value : 0.472         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.535         
#>    Detection Prevalence : 0.893         
#>       Balanced Accuracy : 0.514         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, KNN_NuTo = summary_table_fun(CM))

5.3.8 CART - unbalanced - Nut

#CART_grid <-  expand.grid(cp = c(0.001,0.005,0.01, 0.015, 0.02, 0.05, 0.1, 0.15, 0.2)) --> confirmed that highest kappa is at cp selected by caret
set.seed(12)
cart_Nut_unbal_fit <- train(rating_bin ~ .,
                  data = train_bin_Nut,
                  method = "rpart",
                  trControl = trCtrl,
                  tuneLength = 10)
cart_Nut_unbal_fit

#> CART 
#> 
#> 7623 samples
#>    4 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   cp        Accuracy  Kappa  
#>   0.001284  0.5838    0.05640
#>   0.001445  0.5863    0.05858
#>   0.001605  0.5891    0.05943
#>   0.001734  0.5883    0.05246
#>   0.001819  0.5880    0.05409
#>   0.001926  0.5880    0.05189
#>   0.002033  0.5893    0.05045
#>   0.002568  0.5872    0.02484
#>   0.002729  0.5911    0.02326
#>   0.003050  0.5932    0.01641
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was cp = 0.00305.

# Get the results for each CP step
cart_Nut_unbal_results <- cart_Nut_unbal_fit$results

cart_Nut_unbal_results %>% 
  ggplot(aes(x=cp, y=Accuracy)) +
  geom_line()+
  labs(x = "CP Parameter", y = "Accuracy", title = "CP Plot")

#Now using the cv to predict test set
cart_Nut_unbal_pred <- predict(cart_Nut_unbal_fit, newdata = test_bin_Nut)
#And looking at the confusion matrix for the predictions using the cv 
CM <- confusionMatrix(reference = test_bin_Nut$rating_bin, data = cart_Nut_unbal_pred)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1502 1038
#>       bad     0    0
#>                                         
#>                Accuracy : 0.591         
#>                  95% CI : (0.572, 0.611)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.509         
#>                                         
#>                   Kappa : 0             
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 1.000         
#>             Specificity : 0.000         
#>          Pos Pred Value : 0.591         
#>          Neg Pred Value :   NaN         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.591         
#>    Detection Prevalence : 1.000         
#>       Balanced Accuracy : 0.500         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, CART_Nut = summary_table_fun(CM))

5.3.9 CART - unbalanced - NuBi

#CART_grid <-  expand.grid(cp = c(0.001,0.005,0.01, 0.015, 0.02, 0.05, 0.1, 0.15, 0.2)) --> confirmed that highest kappa is at cp selected by caret
set.seed(12)
cart_NuBi_unbal_fit <- train(rating_bin ~ .,
                  data = train_bin_NuBi,
                  method = "rpart",
                  trControl = trCtrl,
                  tuneLength = 10)
cart_NuBi_unbal_fit

#> CART 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   cp        Accuracy  Kappa   
#>   0.001284  0.5839    0.049008
#>   0.001364  0.5840    0.048006
#>   0.001445  0.5838    0.047922
#>   0.001498  0.5830    0.045608
#>   0.001846  0.5852    0.049754
#>   0.002354  0.5859    0.043717
#>   0.002889  0.5877    0.046967
#>   0.003210  0.5877    0.043065
#>   0.005457  0.5915    0.020972
#>   0.007223  0.5894    0.009009
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was cp = 0.005457.

# Get the results for each CP step
cart_NuBi_unbal_results <- cart_NuBi_unbal_fit$results

cart_NuBi_unbal_results %>% 
  ggplot(aes(x=cp, y=Accuracy)) +
  geom_line()+
  labs(x = "CP Parameter", y = "Accuracy", title = "CP Plot")

#Now using the cv to predict test set
cart_NuBi_unbal_pred <- predict(cart_NuBi_unbal_fit, newdata = test_bin_NuBi)
#And looking at the confusion matrix for the predictions using the cv 
CM <- confusionMatrix(reference = test_bin_NuBi$rating_bin, data = cart_NuBi_unbal_pred)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1377  919
#>       bad   125  119
#>                                        
#>                Accuracy : 0.589        
#>                  95% CI : (0.57, 0.608)
#>     No Information Rate : 0.591        
#>     P-Value [Acc > NIR] : 0.604        
#>                                        
#>                   Kappa : 0.036        
#>                                        
#>  Mcnemar's Test P-Value : <2e-16       
#>                                        
#>             Sensitivity : 0.917        
#>             Specificity : 0.115        
#>          Pos Pred Value : 0.600        
#>          Neg Pred Value : 0.488        
#>              Prevalence : 0.591        
#>          Detection Rate : 0.542        
#>    Detection Prevalence : 0.904        
#>       Balanced Accuracy : 0.516        
#>                                        
#>        'Positive' Class : good         
#> 

summary_table_unbal <- cbind(summary_table_unbal, CART_NuBi = summary_table_fun(CM))

5.3.10 CART - unbalanced - NuTo

#CART_grid <-  expand.grid(cp = c(0.001,0.005,0.01, 0.015, 0.02, 0.05, 0.1, 0.15, 0.2)) --> confirmed that highest kappa is at cp selected by caret
set.seed(12)
cart_NuTo_unbal_fit <- train(rating_bin ~ .,
                  data = train_bin_NuTo,
                  method = "rpart",
                  trControl = trCtrl,
                  tuneLength = 10)
cart_NuTo_unbal_fit

#> CART 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Resampling results across tuning parameters:
#> 
#>   cp        Accuracy  Kappa  
#>   0.001445  0.5878    0.06262
#>   0.001498  0.5861    0.05752
#>   0.001605  0.5881    0.05903
#>   0.001766  0.5885    0.06038
#>   0.001926  0.5870    0.05717
#>   0.002247  0.5876    0.04742
#>   0.002408  0.5886    0.04678
#>   0.002568  0.5886    0.04678
#>   0.003050  0.5881    0.05055
#>   0.004173  0.5911    0.02112
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was cp = 0.004173.

# Get the results for each CP step
cart_NuTo_unbal_results <- cart_NuTo_unbal_fit$results

cart_NuTo_unbal_results %>% 
  ggplot(aes(x=cp, y=Accuracy)) +
  geom_line()+
  labs(x = "CP Parameter", y = "Accuracy", title = "CP Plot")

#Now using the cv to predict test set
cart_NuTo_unbal_pred <- predict(cart_NuTo_unbal_fit, newdata = test_bin_NuTo)
#And looking at the confusion matrix for the predictions using the cv 
CM <- confusionMatrix(reference = test_bin_NuTo$rating_bin, data = cart_NuTo_unbal_pred)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good  bad
#>       good 1502 1038
#>       bad     0    0
#>                                         
#>                Accuracy : 0.591         
#>                  95% CI : (0.572, 0.611)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.509         
#>                                         
#>                   Kappa : 0             
#>                                         
#>  Mcnemar's Test P-Value : <2e-16        
#>                                         
#>             Sensitivity : 1.000         
#>             Specificity : 0.000         
#>          Pos Pred Value : 0.591         
#>          Neg Pred Value :   NaN         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.591         
#>    Detection Prevalence : 1.000         
#>       Balanced Accuracy : 0.500         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_unbal <- cbind(summary_table_unbal, CART_NuTo = summary_table_fun(CM))

5.4.1 Random Forest - balanced - Nut

Hyperparameters

Best tune: mtry = 2

Accuracy metrics

• ACC 53.8
• BACC 53.8
• Kappa 7.40
• Recall 53.9

set.seed(12)
rf_Nut_fit <- caret::train(rating_bin ~ .,
                     data = train_bin_Nut,
                     method = "rf",
                     trControl = trCtrl_down,
                     tuneLength = 10)

#> note: only 3 unique complexity parameters in default grid. Truncating the grid to 3 .

#show the random forest with cv 
rf_Nut_fit

#> Random Forest 
#> 
#> 7623 samples
#>    4 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Addtional sampling using down-sampling
#> 
#> Resampling results across tuning parameters:
#> 
#>   mtry  Accuracy  Kappa  
#>   2     0.5310    0.06036
#>   3     0.5247    0.05028
#>   4     0.5229    0.04546
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was mtry = 2.

plot(rf_Nut_fit, main = "Plot of CV Accuracy relative to Mtry parameter")

set.seed(12)
#make predictions
rf_Nut_pred <- predict(rf_Nut_fit, newdata = test_bin_Nut)

#confusion matrix 
CM <- confusionMatrix(data = rf_Nut_pred, reference = test_bin_Nut$rating_bin)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good bad
#>       good  806 480
#>       bad   696 558
#>                                         
#>                Accuracy : 0.537         
#>                  95% CI : (0.517, 0.557)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 1             
#>                                         
#>                   Kappa : 0.072         
#>                                         
#>  Mcnemar's Test P-Value : 3.62e-10      
#>                                         
#>             Sensitivity : 0.537         
#>             Specificity : 0.538         
#>          Pos Pred Value : 0.627         
#>          Neg Pred Value : 0.445         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.317         
#>    Detection Prevalence : 0.506         
#>       Balanced Accuracy : 0.537         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_down <- cbind(summary_table_down, RF_Nut = summary_table_fun(CM))

5.4.2 Random Forest - balanced - NuBi

Hyperparameters

Best tune: mtry = 3

Accuracy metrics

• ACC 54.8
• BACC 54.2
• Kappa 8.20
• Recall 57.7

set.seed(12)
rf_NuBi_fit <- caret::train(rating_bin ~ .,
                     data = train_bin_NuBi,
                     method = "rf",
                     trControl = trCtrl_down,
                     tuneLength = 10)
#show the random forest with cv 
rf_NuBi_fit

#> Random Forest 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Addtional sampling using down-sampling
#> 
#> Resampling results across tuning parameters:
#> 
#>   mtry  Accuracy  Kappa  
#>    2    0.5512    0.09826
#>    3    0.5569    0.10237
#>    5    0.5490    0.09099
#>    7    0.5452    0.08598
#>    9    0.5472    0.08937
#>   10    0.5478    0.08876
#>   12    0.5482    0.09350
#>   14    0.5437    0.08312
#>   16    0.5403    0.07545
#>   18    0.5423    0.08035
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was mtry = 3.

plot(rf_NuBi_fit, main = "Plot of CV Accuracy relative to Mtry parameter")

set.seed(12)
#make predictions
rf_NuBi_pred <- predict(rf_NuBi_fit, newdata = test_bin_NuBi)

#confusion matrix 
CM <- confusionMatrix(data = rf_NuBi_pred, reference = test_bin_NuBi$rating_bin)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good bad
#>       good  867 513
#>       bad   635 525
#>                                         
#>                Accuracy : 0.548         
#>                  95% CI : (0.528, 0.568)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.999995      
#>                                         
#>                   Kappa : 0.082         
#>                                         
#>  Mcnemar's Test P-Value : 0.000355      
#>                                         
#>             Sensitivity : 0.577         
#>             Specificity : 0.506         
#>          Pos Pred Value : 0.628         
#>          Neg Pred Value : 0.453         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.341         
#>    Detection Prevalence : 0.543         
#>       Balanced Accuracy : 0.542         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_down <- cbind(summary_table_down, RF_NuBi = summary_table_fun(CM))

5.4.3 Random Forest - balanced - NuTo

Hyperparameters

Best tune: mtry = 2

Accuracy metrics

• ACC 56.4
• BACC 55.8
• Kappa 11.3
• Recall 59.3

set.seed(12)
rf_NuTo_fit <- caret::train(rating_bin ~ .,
                     data = train_bin_NuTo,
                     method = "rf",
                     trControl = trCtrl_down,
                     tuneLength = 10)
#show the random forest with cv 
rf_NuTo_fit

#> Random Forest 
#> 
#> 7623 samples
#>   18 predictor
#>    2 classes: 'good', 'bad' 
#> 
#> No pre-processing
#> Resampling: Cross-Validated (5 fold) 
#> Summary of sample sizes: 6099, 6099, 6098, 6098, 6098 
#> Addtional sampling using down-sampling
#> 
#> Resampling results across tuning parameters:
#> 
#>   mtry  Accuracy  Kappa  
#>    2    0.5586    0.10858
#>    3    0.5545    0.09957
#>    5    0.5515    0.09524
#>    7    0.5511    0.09567
#>    9    0.5498    0.09433
#>   10    0.5521    0.09823
#>   12    0.5546    0.10354
#>   14    0.5468    0.08888
#>   16    0.5504    0.09405
#>   18    0.5482    0.09194
#> 
#> Accuracy was used to select the optimal model using the
#>  largest value.
#> The final value used for the model was mtry = 2.

plot(rf_NuTo_fit, main = "Plot of CV Accuracy relative to Mtry parameter")

set.seed(12)
#make predictions
rf_NuTo_pred <- predict(rf_NuTo_fit, newdata = test_bin_NuTo)

#confusion matrix 
CM <- confusionMatrix(data = rf_NuTo_pred, reference = test_bin_NuTo$rating_bin)
CM

#> Confusion Matrix and Statistics
#> 
#>           Reference
#> Prediction good bad
#>       good  887 496
#>       bad   615 542
#>                                         
#>                Accuracy : 0.563         
#>                  95% CI : (0.543, 0.582)
#>     No Information Rate : 0.591         
#>     P-Value [Acc > NIR] : 0.9985        
#>                                         
#>                   Kappa : 0.111         
#>                                         
#>  Mcnemar's Test P-Value : 0.0004        
#>                                         
#>             Sensitivity : 0.591         
#>             Specificity : 0.522         
#>          Pos Pred Value : 0.641         
#>          Neg Pred Value : 0.468         
#>              Prevalence : 0.591         
#>          Detection Rate : 0.349         
#>    Detection Prevalence : 0.544         
#>       Balanced Accuracy : 0.556         
#>                                         
#>        'Positive' Class : good          
#> 

summary_table_down <- cbind(summary_table_down, RF_NuTo = summary_table_fun(CM))